Abstract:

Recent developments in the areas of learning theory and the
geometry of data will be discussed. One will see how these
subjects contribute towards a mathematical foundations of
immunology.

Professor Smale spent the main part of his career at the
University of California, Berkeley. He was awarded the Fields
Medal in 1966. He retired from UC Berkeley in 1995, moving
to a professorship at the City University of Hong Kong. In
2007 he was awarded the Wolf Prize in Mathematics. He is one
of only twelve Fields Medalists to win both prizes. Since
2009 he has been a University Distinguished Professor at the
City University of Hong Kong.

In 1998 Professor Smale compiled a list of 18 problems in
mathematics to be solved in the 21st century, known as Smale's
problems. The list was created in the spirit of Hilbert's
famous list of problems produced in 1900. In fact, Smale's
list contains some of the original Hilbert problems, including
the Riemann hypothesis and the second half of Hilbert's sixteenth
problem, both of which are still unsolved. Other famous problems
on his list include the Poincaré conjecture, which
has recently been solved by Grigori Perelman, the P = NP problem,
and the Navier-Stokes equations, all of which have been designated
Millennium Prize Problems by the Clay Mathematics Institute.